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Please Solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Exercise Fill in the blanks Question 1: Maths Textbook solution.

Answers (1)

The value of a for the function increasing on R is \left ( -\infty ,-1 \right )

Hint: The function f\left ( x \right ) is increasing if f'\left ( x \right )>0

Given: f\left ( x \right )=\sin x-ax+b

Explanation: It is given that

f\left ( x \right )=\sin x-ax+b

f'\left ( x \right )=\cos x-a

\because f\left ( x \right ) is increasing or R

\Rightarrow \cos x-a>0\forall x

\Rightarrow \cos x>a

\Rightarrow a should be less than minimum value of \cos x

i.e;  a<-1

\therefore a\epsilon \left ( -\infty ,-1 \right )

So, the value of a for the function increasing on R are at \left ( -\infty ,-1 \right )

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